Reshuffle Comes After Socialists Suffer Stinging Defeat in Local Elections

PARIS—France's President François Hollande picked a new prime minister on Monday in a bid to steady his authority after his government was rocked by a stinging defeat in local elections.

Facing what has become the deepest crisis in his nearly two years in office, Mr. Hollande went on national television to announce the replacement of Prime Minister Jean-Marc Ayrault, one of his closest allies, by Manuel Valls, a politically savvy...